I could be lost here.

Do the Federal American Eagle .223 training round have a smaller primer pocket than normal?

If so, is there a way around this problem?

I can't say on that paticular round, but, military brass has the primer swaged into place, which can make the primer pocket appear and feel to be small. When reloading such brass, you need to swage or cut out the brass that is formed by the crimp. It can also be a real bugger depriming crimped brass, with the depriming pin often punching through the primer cup as opposed to removing the primer.

Yeah. After searching around a bit... ...seems like I need a RCBS primer pocket swadger.

Do you need to size your brass first with this? Or is sizing second?

Is a primer pockets reamer the same thnig, like the lee or lyman?

p67
I think that these rounds are mil spec as was already mentioned. The primers are crimped in.
To reload you need to remove the crimp.
There are two different ways to do this. One is to cut the crimp at the casehead. The second is to push the brass backout of the way. Reamers are cutting tools. Swagers are pushing tools.

This process needs to be done after the old primer is removed You can resize first or you can use a universal decaping die. Lee and RCBS both offer this tool.

I hope this helps.

muck

I have a Lyman pocket reamer tool. Works fine. Just need to sit down with one bucket on one side and another on the other and get into it!! Seems to work okay, nice tight primers.

Cheers